Generalized Stabilizing Conditions for Model Predictive Control

© 2015, The Author(s).This note addresses the tracking problem for model predictive control. It presents simple procedures for both linear and nonlinear constrained model predictive control when the desired equilibrium state is any point in a specified set. The resultant region of attraction is the union of the regions of attraction for each equilibrium state in the specified set and is therefore larger than that obtained when conventional model predictive control is employed

Robust Tracking Commitment with Application to Demand Response

Many engineering problems that involve hierarchical control applications, such as demand side ancillary service provision to the power grid, can be posed as an optimal tracking commitment problem. In this setting, the lower- level controller commits a set of possible reference trajectories over a finite horizon to an external entity, which requires guaranteed tracking of any reference trajectory that can be sampled from the committed set, with an allowed deviation, in exchange for a payment corresponding to the size of the reference set. This paper presents a method to solve the optimal tracking commitment problem for constrained linear systems subject to uncertain disturbance and reference signals. The proposed method allows tractable computations via convex optimization for conic representable reference sets and lends itself to distributed solution methods. We demonstrate the proposed method in a simulation based case study with a commercial building that offers a frequency regulation service to the power grid

Predictive Control methods for Building Control and Demand Response

This thesis studies advanced control techniques for the control of building heating and cooling systems to provide demand response services to the power network. It is divided in three parts. The first one introduces the MATLAB toolbox OpenBuild which aims at facilitating the design and validation of predictive controllers for building systems. In particular, the toolbox constructs models of building that are appropriate for use in predictive controllers, based on standard building description data files. It can also generate input data for these models that allows to test controllers in a variety of weather and usage scenarios. Finally, it offers co-simulation capability between MATLAB and EnergyPlus in order to test the controllers in a trusted simulation environment, making it a useful tool for control engineers and researchers who want to design and test building controllers in realistic simulation scenarios. In the second part, the problem of robust tracking commitment is formulated: it consists of a multi-stage robust optimization problem for systems subject to uncertainty where the set where the uncertainty lies is part of the decision variables. This problem formulation is inspired by the need to characterize how an energy system can modify its electric power consumption over time in order to procure a service to the power network, for example Demand Response or Reserve Provision. A method is proposed to solve this problem where the key idea is to modulate the uncertainty set as the image of a fixed uncertainty set by a modifier function, which allows to embed the modifier function in the controller and by doing so convert the problem into a standard robust optimization problem. The applicability of this framework is demonstrated in simulation on a problem of reserve provision by a building. We finally detail how to derive infinite horizon guarantees for the robust tracking commitment problem. The third part of thesis reports the experimental works that have been conducted on the Laboratoire d'Automatique Demand Response (LADR) platform, a living lab equipped with sensors and a controllable heating system. These experiments implement the algorithms developed in the second part of the thesis to characterize the LADR platform flexibility and demonstrate the closed-loop control of a building heating system providing secondary frequency control to the Swiss power network. In the experiments, we highlight the importance of being able to adjust the power consumption baseline around which the flexibility is offered in the intraday market and show how flexibility and comfort trade off

Improving Tracking in Optimal Model Predictive Control

The thesis deals with the improvement in the tracking in model predictive control(MPC). The main motivation is to explore high embedding performance controllers with constraint handling capabilities in a simple fashion. There are several techniques available for effectively using an infinite horizon rather than a finite horizon. First, there has been relatively little discussion so far on how to make effective use of advance information on target changes in the predictive control literature. While earlier work has indicated that the default solutions from conventional algorithms are often poor, very few alternatives have been proposed. This thesis demonstrates the impact of future information about target changes on performance, and proposes a pragmatic method for identifying the amount of future information on the target that can be utilised effectively in infinite horizon algorithms. Numerical illustrations in MATLAB demonstrate that the proposal is both systematic and beneficial. This thesis introduces several important issues related to model predictive control (MPC)tracking that have been hitherto neglected in the literature, by first deriving a control law for future information about target changes within optimal predictive control (OMPC) for both nominal and constraints cases. This thesis proposes a pragmatic design for scenarios in which the target is unreachable. In order to deal with an unreachable target, the proposed design allows an artificial target into the MPC optimisation problem. Numerical illustrations in MATLAB provide evidence of the efficacy of the proposals. This thesis extends efficient, robust model predictive control (MPC) approaches for Linear Parameter-Varying (LPV) systems to tracking scenarios. A dual-mode approach is used and future information about target changes is included in the optimisation tracking problem. The controller guarantees recursive feasibility by adding an artificial target as an extra degree of freedom. Convergence to admissible targets is ensured by constructing a robustly invariant set to track any admissible target. The efficacy of the proposed algorithm is demonstrated by MATLAB simulation. The thesis considers the tractability of parametric solvers for predictive control based optimisations, when future target information is incorporated. It is shown that the inclusion of future target information can significantly increase the implied parametric dimension to an extent that is undesirable and likely to lead to intractable problems. The thesis then proposes some alternative methods for incorporating the desired target information, while minimising the implied growth in the parametric dimensions, at some possibly small cost to optimality. Feasibility is an important issue in predictive control, but the influence of many important parameters such as the desired steady-state, the target and the current value of the input is rarely discussed in the literature. At this point, the thesis makes two contributions. First, it gives visibility to the issue that including the core parameters, such as the target and the current input, vastly increases the dimension of the parametric space, with possible consequences on the complexity of any parametric solutions. Secondly, it is shown that a simple re-parametrization of the degrees of freedom to take advantage of allowing steady-state offset can lead to large increases in the feasible volumes, with no increases in the dimension of the required optimisation variables. Simulation with MAT LAB 2017a provides the evidence of the efficacy of all proposals

Model predictive control for tracking random references,”

This paper proposes a model predictive control scheme for tracking a-priori unknown references varying in a wide range and analyzes its performance. It is usual to assume that the reference eventually converges to a constant in which case convergence to zero of the tracking error can be established. In this note we remove this simplifying assumption and characterize the set to which the tracking error converges and the associated region of convergence